Ivan H. Deutsch

Can one trust quantum simulators

Various fundamental phenomena of strongly correlated quantum systems such as high-T(c) superconductivity, the fractional quantum-Hall effect and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models which are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper (Feynman 1982 Int. J. Theor. Phys. 21 467), Richard Feynman suggested that such models might be solved by simulation with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a quantum simulator, would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question Can we trust quantum simulators? is … to some extent.

Entangling atomic spins with a Rydberg-dressed spin-flip blockade

Controlling quantum entanglement between parts of a many-body system is the key to unlocking the power of quantum information processing for applications such as quantum computation, highprecision sensing, and simulation of many-body physics. Spin degrees of freedom of ultracold neutral atoms in their ground electronic state provide a natural platform given their long coherence times and our ability to control them with magneto-optical fields, but creating strong coherent coupling between spins has been challenging. We demonstrate a Rydberg-dressed ground-state blockade that provides a strong tunable interaction energy (∼1 MHz in units of Planck’s constant) between spins of individually trapped cesium atoms. With this interaction we directly produce Bell-state entanglement between two atoms with a fidelity ≥ 81(2)%, excluding atom loss events, and ≥ 60(3)% when loss is included.

Quantum process tomography of unitary and near-unitary maps

Center for Quantum Information and Control, MSC07{4220,University of New Mexico, Albuquerque, New Mexico 87131-0001, USA(Dated: July 25, 2014)We study quantum process tomography given the prior information that the map is a unitary orclose to a unitary process. We show that a unitary map on a d-level system is completely char-acterized by a minimal set of d

Quantum tomography protocols with positivity are compressed sensing protocols

Compressed sensing (CS) is a technique to faithfully estimate an unknown signal from relatively few data points when the measurement samples satisfy a restricted isometry property (RIP). Recently, this technique has been ported to quantum information science to perform tomography with a substantially reduced number of measurement settings. In this work we show that the constraint that a physical density matrix is positive semidefinite provides a rigorous connection between the RIP and the informational completeness of a POVM used for state tomography. This enables us to construct informationally complete measurements that are robust to noise using tools provided by the CS methodology. The exact recovery no longer hinges on a particular convex optimization program; solving any optimization, constrained to the cone of positive semidefinite matrices, effectively results in a CS estimation of the state. From a practical point of view, we can therefore employ fast algorithms developed to handle large dimensional matrices for efficient tomography of quantum states of a large dimensional Hilbert space.

Robust quantum logic in neutral atoms via adiabatic Rydberg dressing

We study a scheme for implementing a controlled-Z (CZ) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground electronic state, we can protect the gate from decoherence due to random phase errors that typically arise because of atomic thermal motion. In addition, the adiabatic protocol allows for a Doppler-free configuration that involves counterpropagating lasers in a σ+/σ- orthogonal polarization geometry that further reduces motional errors due to Doppler shifts. The residual motional error is dominated by dipole-dipole forces acting on doubly-excited Rydberg atoms when the blockade is imperfect. As a result, for reasonable parameters, with qubits encoded into the clock states of 133Cs, we predict that our protocol could produce a CZ gate in < 10 μs with error probability on the order of 10-3.

Enhanced Squeezing of a Collective Spin via Control of Its Qudit Subsystems

Unitary control of qudits can improve the collective spin squeezing of an atomic ensemble. Preparing the atoms in a state with large quantum fluctuations in magnetization strengthens the entangling Faraday interaction. The resulting increase in interatomic entanglement can be converted into metrologically useful spin squeezing. Further control can squeeze the internal atomic spin without compromising entanglement, providing an overall multiplicative factor in the collective squeezing. We model the effects of optical pumping and study the tradeoffs between enhanced entanglement and decoherence. For realistic parameters we see improvements of ~10 dB.

Quantum tomography of the full hyperfine manifold of atomic spins via continuous measurement on an ensemble

Quantum state reconstruction based on weak continuous measurement has the advantage of being fast, accurate and almost non-perturbative. In this work we present a pedagogical review of the protocol proposed by Silberfarb et al (2005 Phys. Rev. Lett. 95 030402), whereby an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner so as to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time through a maximum-likelihood estimate. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sublevels of a large-spin alkali atom, 133Cs. We detail two different protocols for control. Using magnetic interactions and a quadratic ac Stark shift, we can reconstruct a chosen hyperfine manifold F, e.g. the seven-dimensional F = 3 manifold in the electronic ground state of Cs. We review the procedure as implemented in experiments (Smith et al 2006 Phys. Rev. Lett. 97 180403). We extend the protocol to the more ambitious case of reconstruction of states in the full 16-dimensional electronic ground subspace (F = 3⊕F = 4), controlled by microwaves and radio-frequency (RF) magnetic fields. We give detailed derivations of all physical interactions, approximations, numerical methods and fitting procedures, tailored to the realistic experimental setting. For the case of light-shift and magnetic control, reconstruction fidelities of ~0.95 have been achieved, limited primarily by inhomogeneities in the light-shift. For the case of microwave/RF-control we simulate fidelity >0.97, limited primarily by signal-to-noise.

Information gain in tomography - A quantum signature of chaos

We find quantum signatures of chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The tomographic measurement record consists of a sequence of expectation values of a Hermitian operator that evolves under repeated application of the Floquet map of the quantum kicked top. We find an increase in information gain and, hence, higher fidelities in the reconstruction algorithm when the chaoticity parameter map increases. The results are well predicted by random matrix theory.

Three-dimensional light-matter interface for collective spin squeezing in atomic ensembles

We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.

Single-shot quantum state estimation via a continuous measurement in the strong backaction regime

Dahlem Center for Complex Quantum Systems,Freie Universitx7fat Berlin, 14195 Berlin, Germany(Dated: June 20, 2014)We study quantum tomography based on a stochastic continuous-time measurement record ob-tained from a probe eld collectively interacting with an ensemble of identically prepared systems.In comparison to previous studies, we consider here the case in which the measurement-inducedbackaction has a nonnegligible e ect on the dynamical evolution of the ensemble. We formulatea maximum likelihood estimate for the initial quantum state given only a single instance of thecontinuous di usive measurement record. We apply our estimator to the simplest problem { statetomography of a single pure qubit, which, during the course of the measurement, is also subjectedto dynamical control. We identify a regime where the many-body system is well approximated at alltimes by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochas-tic evolution. We simulate the results of our estimator and show that we can achieve close to theupper bound of delity set by the optimal POVM. This estimate is compared to, and signi cantlyoutperforms, an equivalent estimator that ignores measurement backaction.